Abstract
Quantum spin models have been studied extensively in one and higher dimensions. Furthermore, these systems have been doped with holes to study models of spin-1/2. Their anyonic counterparts can be built from non-Abelian anyons, such as Fibonacci anyons described by theories, which are quantum deformations of the algebra. Inspired by the physics of spins, several works have explored ladders of Fibonacci anyons and also one-dimensional (1D) models. Here, we aim to explore the combined effects of extended dimensionality and doping by studying ladders composed of coupled chains of interacting itinerant Fibonacci anyons. We show analytically that in the limit of strong rung couplings these models can be mapped onto effective 1D models. These effective models can either be gapped models of hole pairs, or gapless models described by (or modified ) chains of Fibonacci anyons, whose spectrum exhibits a fractionalization into charge and anyon degrees of freedom. The charge degrees of freedom are described by the hardcore boson spectra while the anyon sector is given by a chain of localized interacting anyons. By using exact diagonalizations for two-leg and three-leg ladders, we show that indeed the doped ladders show exactly the same behavior as that of chains. In the strong ferromagnetic rung limit, we can obtain a new model that hosts two different kinds of Fibonacci particles, which we denote as the heavy 's and light 's. These two particle types carry the same (non-Abelian) topological charge but different (Abelian) electric charges. Once again, we map the two-dimensional ladder onto an effective chain carrying these heavy and light 's. We perform a finite size scaling analysis to show the appearance of gapless modes for certain anyon densities, whereas a topological gapped phase is suggested for another density regime.
17 More- Received 24 August 2015
- Revised 22 November 2015
DOI:https://doi.org/10.1103/PhysRevB.93.035124
©2016 American Physical Society